Choose a mode, enter values, then press Calculate. The form uses a responsive grid: three columns on large screens, two on smaller, one on mobile.
Koschmieder’s law links meteorological visibility range V to the atmospheric extinction coefficient β and contrast threshold ε:
- V = ln(1/ε) / β
- β = ln(1/ε) / V
- ε = e−βV
Here, β is the total extinction (scattering + absorption). With ε = 0.02, ln(1/ε) ≈ 3.912, so visibility simplifies to V ≈ 3.912/β when β is in 1/km.
- Select the mode that matches your available measurements.
- Enter values with consistent units, then pick units from dropdowns.
- Use ε = 0.02 for standard visibility reporting, if needed.
- Optionally enter a path length to estimate transmittance T.
- Press Calculate to show results above the form.
- Use the CSV/PDF buttons to export the computed table.
If you are using a sensor that reports β in 1/m, select the 1/m option. The calculator converts internally to 1/km for consistent formulas.
These examples use ε = 0.02 (K ≈ 3.912). Values are illustrative.
| Extinction β (1/km) | Visibility V (km) | Notes |
|---|---|---|
| 0.10 | 39.12 | Very clear air; long-range visibility. |
| 0.50 | 7.824 | Moderate haze; common urban conditions. |
| 1.00 | 3.912 | Hazy air; reduced visibility for driving. |
| 2.00 | 1.956 | Dense haze; poor visibility and contrast. |
1) Why Koschmieder visibility matters
Visibility is a safety and performance metric for transport, fieldwork, and imaging. A change from 10 km to 2 km can alter braking distance needs, aviation minima, maritime lookout range, and camera exposure choices. This calculator converts between extinction and reported visibility so teams can compare measurements and observations consistently.
2) Key constants and common reporting thresholds
Many meteorological services use a contrast threshold ε = 0.02 for standard visibility, which yields K = ln(1/ε) ≈ 3.912. That constant turns a measured extinction coefficient into a practical range estimate. For example, β = 0.50 1/km gives V ≈ 7.8 km, while β = 2.00 1/km gives V ≈ 2.0 km.
3) Extinction coefficient interpretation
The extinction coefficient β represents total attenuation of a light beam by scattering and absorption. In many outdoor conditions, scattering dominates, but absorption can matter in smoke, dust, or industrial plumes. Instruments may estimate β from backscatter, transmissometers, or nephelometers, and units may be reported as 1/m or 1/km.
4) Unit handling and conversion confidence
This calculator converts all inputs to an internal 1/km basis before applying Koschmieder’s law. A value of 0.001 1/m equals 1.0 1/km, which is a useful quick check. Visibility output can be shown in meters, kilometers, or miles to match road reporting, airport METAR conventions, or field logs.
5) Using transmittance as a quality check
When you enter an optional path length x, the calculator also reports transmittance T = e−βx. This helps assess how quickly contrast collapses over a given line of sight. For example, with β = 1.0 1/km, a 2 km path gives T ≈ e−2 ≈ 0.135, meaning only about 13.5% of beam intensity remains.
6) Typical ranges in real environments
Clear rural air can show β near 0.05–0.20 1/km (visibility tens of kilometers). Urban haze can push β toward 0.30–1.00 1/km (visibility roughly 4–13 km). Dense haze or smoke may exceed β = 2.0 1/km (visibility near 2 km or less). Local humidity, aerosols, and wind drive these shifts.
7) Choosing ε for human and camera systems
Contrast threshold depends on observer sensitivity and target/background contrast. Human vision under daylight often aligns with ε around 0.02 for standardized reporting, but imaging systems may use different thresholds due to sensor noise, optics, and post-processing. If your protocol specifies ε, enter it directly to keep results traceable.
8) Good practice for reporting and auditing
Record the measurement method, averaging period, location, and time, then export results using the CSV/PDF buttons for documentation. Include β units and the ε assumption, because changing ε changes K and therefore visibility. For multi-site studies, use the same ε and unit convention to avoid systematic bias.
1) What does ε represent in visibility calculations?
ε is the contrast threshold, the smallest contrast you consider detectable. Lower ε means stricter detection, producing a larger K and a longer reported visibility for the same extinction.
2) Why is ε = 0.02 used so often?
ε = 0.02 is a widely used standard for meteorological visibility reporting. It gives K ≈ 3.912, enabling direct comparison across stations and studies when the same assumption is used.
3) My instrument reports β in 1/m. What should I do?
Select the 1/m unit and enter the reported value. The calculator converts internally to 1/km. As a check, 0.001 1/m equals 1.0 1/km.
4) Is β the same as scattering only?
No. β is total extinction, including scattering and absorption. In haze, scattering often dominates, but smoke or soot can add absorption that lowers visibility more than scattering alone.
5) What does the transmittance output tell me?
Transmittance T = e−βx estimates how much light intensity remains after traveling distance x. It is a practical way to assess contrast loss over a chosen line-of-sight distance.
6) Can I use this for roadway and aviation visibility?
Yes, as long as you understand the assumption behind ε and how β was measured. Use consistent thresholds and units, and report the method so results remain comparable across situations.
7) Why might observed visibility differ from calculated visibility?
Visibility observations depend on target contrast, background lighting, observer position, and local inhomogeneity. Instrument β may represent a different path or averaging period than the visual line of sight.